Probabilistic Models for distributed and concurrent systems. Limit
theorems and applications to statistical parameter estimation
Samy Abbes, PhD Thesis - supervised by Albert Benveniste
Concurrent systems possess local state
and partially ordered time. Their semantics is typically formulated in
terms of traces and event structures. Probabilistic models for such
systems
are proposed, for which concurrent processes are independent in the
probabilistic
sense. Markov nets are proposed as a probabilistic model for safe Petri
nets, following this philosophy. For such systems, a Markov property is
proved, with application to recurrence theory. Finally a law of large
numbers
is proved for concurrent systems exhibiting enough synchronization.
Applications
to statistical parameter estimation are given.
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